Related papers: Discrete localities II
In this paper we study the lattice point covering property of some regular polygons in dimension 2.
We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the poly-disc. Finally, we compare the framework developed here…
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…
In this paper we continue to study the property of separability of functional space C(X) with the open-point and bi-point-open topologies.
This is a continuation of "Mirror Principle III"(math.AG/9912038).
The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…
In \cite{X-Z DCS1}, we introduced discrete conformal structures on surfaces with boundary via an axiomatic framework, and provided a classification of such discrete conformal structures. The present work focuses on the rigidity and…
This paper considers the question of which continua are 2-to-1 retracts of continua.
The continued fraction mapping maps a number in the interval $[0,1)$ to the sequence of its partial quotients. When restricted to the set of irrationals, which is a subspace of the Euclidean space $\mathbb{R}$, the continued fraction…
This paper is concerned with developing a 2-dimensional analogue of the notion of an ordinary discrete fibration. A definition is proposed, and it is shown that such discrete 2-fibrations correspond via a 2-equivalence to certain…
We obtain a complete classification of hypercomplex manifolds, on which a compact group of automorphisms acts transitively. The description of the spaces as well as the proofs of our results use only the structure theory of reductive…
We describe two types of localization for $(\infty, 1)$-categories which determine the successive terms in the homotopy spectral sequence of a (co)simplicial object.
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
A semi-discretization in time, according to a full implicit Euler scheme, for a 2D dissipative quasi geostrophic equation, is studied. We prove existence, uniqueness and regularity results of the solution to the predicted discretization, in…
Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional…
This second part of the paper strengthens the descent theory described in the first part to rational maps, arbitrary base fields, and dynamics given by correspondences. We obtain in particular a decomposition of any difference field…
Ap\'ery's remarkable discovery of rapidly converging continued fractions with small coefficients for $\zeta(2)$ and $\zeta(3)$ has led to a flurry of important activity in an incredible variety of different directions. Our purpose is to…
We construct an enlargement of the classifying space of mixed Hodge structures with polarized graded quotients, by adding mixed Hodge theoretic version of SL(2)-orbits. This space has a real analytic structure and a log structure with sign.…
In a preceding article, we have studied a generalization of the problem of finding a martingale on a manifold whose terminal value is known. This article completes the results obtained in the first article by providing uniqueness and…
We give a moderately motivated exposition of exponentiable locales and the construction of exponentials in $\textsf{Loc}$, without assuming prior knowledge of exponential topological spaces or continuous posets.